A stochastic formulation to Telegrapher´s Equation in higher dimensions

Accuracy of Kac´s telegrapher´s process approach for the non-zero velocity was demonstrated. Although this process can recover ID TE and other boundary conditions for this approach can be developed, the approach could not be applied in higher dimensions. Although Kac´s randomized wave equation solution meets analytical TE solution in higher dimensions as well, we did not mention it since it does not avoid solving the wave equation which is no easier than solving TE. The PRW on the other hand also governs ID TE in the continuum limit, but not in 2D. We showed that Plyukhin´s modification to the state transitions reads, i.e. the probabilities of states at a time step depend also on cross derivative terms at the previous step. A test case to validate the modified PRW model is the simple 2D wave propagation in free-space. The free-space Green´s function solution for an impulse excited at time t = 0 from the origin of the xy plane is demonstrated. Corresponding stochastic solution to the above case along with the case with partially reflecting/absorbing boundary conditions will be demonstrated at the symposium.